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In this work we investigate buckling of compressed elastic thin films, which are bonded onto a viscous layer of finite thickness. It is found that the normal stress exerted by the viscous layer on the elastic film evolves with time showing a minimum at early buckling stages, while it increases at later stages. The normal stress also shows a minimum as a function of applied compressive stress, which depends strongly on the viscosity of the underlying layer and strain values. Furthermore, with decreasing viscosity the film roughness amplitude also shows a minimum at early buckling stages. The effect of the viscosity becomes more pronounced with increasing strain in the film. Finally, decreasing elastic film thickness and/or increasing viscous layer thickness also enhance buckling roughness. © 2003 American Institute of Physics.